Question 1177505


let  the price of coffee be {{{c}}}, sugar {{{s}}}, and  flour {{{f}}}

if Diana bought {{{4 }}}pounds of coffee, {{{5 }}}pounds of sugar, and {{{10}}} pounds of flour and received ${{{2.25}}} change from ${{{30}}}, we have

{{{4c+5s+10f +2.25=30}}}............1)

find the price for each pound of coffee, sugar, and flour:


given: {{{9}}} pounds of flour is ${{{0.50}}} more than {{{5}}} pounds of sugar 

{{{9f=5s+.50}}}
{{{f=(5s+.50)/9}}}..........a)

{{{10}}} pounds of flour and {{{4}}} pounds of sugar cost ${{{2 }}}more than {{{3}}} pounds of coffee

{{{10f+4s=3c+2}}}
{{{f=(3c-4s+2)/10}}}..........b)

from a) and b) we have

{{{(5s+.50)/9=(3c-4s+2)/10}}}

{{{10(5s+.50)=9(3c-4s+2)}}}

{{{50s+5=27c-36s+18}}}

{{{50s+36s=27c+18-5}}}

{{{86s=27c+13}}}

{{{s=(27c+13)/86}}}..........c)

go to a), substitute {{{s}}}

{{{f=(5(27c+13)/86+.50)/9}}}..........a)

go to

{{{4c+5s+10f +2.25=30}}}............1), substitute {{{s}}} and {{{f}}}

{{{4c+5(27c+13)/86+10(5(27c+13)/86+.50)/9+2.25=30}}}

{{{(629c)/86 - 25.5988 = 0}}}

{{{c=  (25.59888*86)/629}}}

{{{c=  3.5}}}

go to  equation  

{{{s=(27*c+13)/86}}}..........c), substitute {{{c}}}
{{{s=(27*3.3+13)/86}}}
{{{s=1.25}}}

do same here

{{{f=(5(27*3.5+13)/86+.50)/9}}}..........a)

{{{f=0.75}}}


the price for each pound of coffee is ${{{3.50}}}, sugar is ${{{1.25}}}, and flour is ${{{0.75}}}

check:

{{{4*3.50+5*1.25+10*0.75+2.25=30}}}
{{{14+6.25+7.5+2.25=30}}}
{{{30=30}}}